Elections and Political Participation - lecture notes

Michał Pierzgalski

This version: November 5, 2018 (This document is a work in progress)

References

See the course syllabus that is available via Moodle e-learning platform: https://moodle.uni.lodz.pl/?lang=en

https://docs.google.com/document/d/1JFKfCKntFD7IqTDogMdiQvNAYtbFWV1jnX3jewbepsQ/edit?usp=sharing

Lecture 1: Preliminaries - Democracy and elections

Introductory question

What is the most fundamental feature/principle of democracy?

Normative and positive statements

In science, statements are broken into two main categories:

Normative and positive statements (2)

Positive political science is the branch of political science that concerns the description and explanation of political phenomena.

Normative and positive statements (3)

Normative and positive statements (4)

Positive statements are either true or false. Before we check whether or not positive statement is true, we call it a hypothesis.

When a hypothesis is positively tested we can say that statement is a theorem or corollary.

Democracy - normative and positive definitions

– (Schumpeter, 1976)

Democracy

Elections

Election is simply a choice. To elect means “to choose or make a decision”.

Partisan and non-partisan elections

IOWA judges selection: https://www.dropbox.com/s/8nrcissdbhym9df/JNP_KnowYourCourts_2015.pdf?dl=0

Direct and representative democracy

Athenian democracy

Figure: Kleroterion - a randomization device used by the Athenians during the period of democracy to select citizens to the boule, to most state offices, to the nomothetai, and to court juries.

Figure: Kleroterion - a randomization device used by the Athenians during the period of democracy to select citizens to the boule, to most state offices, to the nomothetai, and to court juries.

Athenian democracy (2)

The Ekklesia (People’s Assembly) became the legislative body of Athens. It was the general meeting of all citizens — males of Athenian origin over the age of 20.

With a few exceptions, all appointments in Athens were made by lot or by rotation to equalize everyone’s opportunity to hold office.

Athenian democracy (3)

Figure: Athenian democracy - the structure of government (Tangian, 2014)

Figure: Athenian democracy - the structure of government (Tangian, 2014)

City-state and nation state

A city-state:

A nation state (or nation-state):

Representative democracy

Representative democracy (2)

Robert Dahl on “realistic” democracy (polyarchy)

Main features:

Larry Diamond on representative democracy

Main features:

Samuel Huntington on democratic government

“… a twentieth-century political system … [is democratic] … to the extent that its most powerful collective decision makers are selected through fair, honest, and periodic elections in which candidates freely compete for votes and in which virtually all the adult population is eligible to vote.”

“Governments produced by elections may be inefficient, corrupt, shortsighted, irresponsible, dominated by special interests, and incapable of adopting policies demanded by the public good. These qualities may make such governments undesirable but they do not make them undemocratic. Democracy is one public virtue, not the only one …”.

Democracy and republic

  1. The term republic today often refers to a representative democracy with an elected head of state, such as a president, serving for a limited term, in contrast to states with a hereditary monarch as a head of state.
  1. James Wilson - “a republican or democratic” government - “the people at large retain the supreme power”.
  1. Today’s modern representative democracies imitate more the Roman Republic than the Greek models because it was a state in which:

Democracy and republic (2)

According to Montesquieu:

[R]epublican government is that in which the body, or only a part of the people, is posessed of the supreme power,

… and thus may be either a democratic or an aristocratic republic.

Democracy and republic (3)

As for the republican form of government, some emphasize “rule of law”: John Adams described a republic as

Principles of Free Elections

The election is considered to be ‘general’ because all citizens have the right to vote - regardless of gender, income, religion, profession or political beliefs. They usually must, however, be aged 18 or over on election day.

The election is ‘secret’ - a voter’s choices in an election or a referendum are both secret and anonymous.

The election is ‘direct’ because the voters elect without an intermediate body.

The election is ‘free’ because citizens may not be influenced or put under pressure regarding their decision on whom to support.

The election is ‘equal’ because each voter is allowed to cast the same numbers of votes.

In fact, it is not usually true that every vote carries the same weight. We will discuss this important issue later.

The growth of universal suffrage in UK

\[**1265**\]

Parliament established. It contains 2 chambers. One is ‘the Lords’ - unelected aristocrats. The other is ‘the Commons’. These Members of Parliament (MPs) are smaller landowners and are elected only by male landowners.

\[**1832**\]

Great Reform Act. Before this time only landowners could vote for MPs to sit in the House of Commons. This meant 1 in 7 men could vote. (440,000 people) After 1832 the male urban middle classes gain the vote, and so the electorate increases to 1 in 5 men (650,000 people). (...)

… The growth of universal suffrage in UK

\[**1867**\]

Second Reform Act. This extends the vote to the skilled urban male working class. The electorate increases to 1 in 3 men.

\[**1884**\]

Third Reform Act. The vote is now given to working class men in the countryside. The electorate is now 2 out of 3 men.

\[**1918**\]

Representation of the People Act. Almost all men over 21 years old, and women over 30 years old now have the vote.

\[**1928**\]

Effectively all women and men over 21 now have the right to vote.

Electoral fraud

What prevents election from being fair and free?

Electoral fraud (2)

The electorate may be poorly informed about issues or candidates due to lack of freedom of the press, lack of objectivity in the press due to state or corporate control, or lack of access to news and political media.

Freedom of speech may be limited by the state, favoring certain viewpoints or state propaganda.

Electoral fraud (3)

Electoral fraud involve e.g. manipulating electoral districts boundaries, exclusion of opposition candidates from eligibility for office, and manipulating thresholds, those in power may arrest or assassinate candidates, outlaw competitors, harass or beat campaign workers, or intimidate voters with violence, tampering with the election mechanism, confusing or misleading voters about how to vote, violation of the secret ballot, tampering with voting machines, destruction of legitimately cast ballots, voter suppression, voter registration fraud, failure to validate voter residency, fraudulent tabulation of results, use of physical force or verbal intimation at polling places, persuading candidates into not standing against them, blackmailing, bribery, carousel voting etc.

Electoral fraud (4)

Carousel voting is a method of vote rigging in elections, used e.g. in Russia and Ukraine. Voters are driven around to cast ballots multiple times. The term "carousel" refers to the circular movement made by the voters, from one polling station to the next, and so on.

Lecture 2: Electoral systems - methods of selection of partisan (political) and nonpartisan officials (part 1)

Collective decisions

Voting is a way to make collective decisions, that is, decisions that are made by a group. There are also other methods to make group decisions - e.g. consensus, random process, sortition, contest.

Consensus

Consensus is a process for group decision-making. It is a method by which an entire group of people can come to an agreement. The input and ideas of all participants are gathered and synthesized to arrive at a final decision acceptable to all.

Collective decisions (2)

Consensus may not be efficient way to make decisions when the group of people who try to select the best option is very large. Consensus may take much more time than voting.

Collective decisions (3)

In voting, everyone expresses their will/opinion (in the form of a vote), which means that voting produces certainty regarding the distribution of preferences. The decision rule is applied to this distribution to determine the collective decision.

For example, in the case of a simple majority vote, the option with the most votes becomes the collective decision.

There are many different methods of selecting using a vote - we discuss some of them in this course.

Voting

Voting has been used as a feature of democracy since the 6th century BC, when democracy was introduced by the Athenians.

However, in Athenian democracy, voting was seen as the least democratic among methods used for selecting public officials, and was little used, because elections were believed to inherently favor the wealthy and well-known over average citizens.

Assemblies open to all citizens, and selection by lot (known as sortition), as well as rotation of office seems to be more democratic for Athenians.

Sortition

Sortition (also known as allotment or the drawing of lots) is the selection of decision makers by lottery. The decision-makers are chosen as a random sample from a larger pool of candidates.

In ancient Athenian democracy, sortition was the primary method for appointing officials, and its use was widely regarded as a principal characteristic of democracy.

Voting (2)

One of the earliest recorded elections in Athens was a plurality vote that it was undesirable to "win": in the process called ostracism, voters chose the citizen they most wanted to exile for ten years.

Most elections in the early history of democracy were held using plurality voting or some variant, but as an exception, the state of Venice in the 13th century adopted the system we now know as approval voting to elect their Great Council.

Voting system

Free and fair elections are a central feature of, and a neccesery condition for, representative democracy.

An electoral system is a set of rules that determine how elections and referendums are conducted and how their results are determined.

Social choice theory

The study of formally defined voting systems is called social choice theory or voting theory, a subfield of political science, economics and mathematics.

Social choice theory is concerned with the study of group decision making processes.

Voting system (2)

A voting system or electoral system is a winner-selection method by which voters make a choice between options, often in an election or on a policy referendum.

In the broad sense of the term, the electoral system is a set of laws that regulate electoral competition between candidates or parties or both.

Voting system (3)

Electoral system comprises three essential elements, namely:

Voting system (4)

Electoral formula is the most important element of a voting system and usually the name of the electoral system is derived from the name of electoral formula.

Voting system - ballot types

We can distinguish two types of ballots - categorical (voters are allowed to choose only one candidate or party) and preferential (voters can rank each candidate in order of preference).

In some voting systems voters are eligible to use both categorical and preferential vote, e.g. voters choose between parties (categorical) and then rank candidates on the chosen party list.

Ballot types (1)

Figure: A state (USA, Texas) ballot paper

Figure: A state (USA, Texas) ballot paper

Ballot types (2)

Figure: A ballot paper used in STV

Figure: A ballot paper used in STV

Ballot types (3)

Figure: A ballot papers used in OLPR and Closed-list PR

Figure: A ballot papers used in OLPR and Closed-list PR

Ballot types (4)

Figure: A ballot papers used in Australian election

Figure: A ballot papers used in Australian election

Ballot types (4b)

Figure: How to vote (Labor party, Australia)

Figure: How to vote (Labor party, Australia)

Ballot paper in Swiss elections - panachage and cumulative voting

Figure: Voting in Swiss elections

Figure: Voting in Swiss elections

Types of voting systems

Electoral systems can be divided into three essential subgroups:

  1. majoritarian voting systems (use majoritarian formulas) - e.g. plurality method, Borda count, Instant Runoff (alternative vote),

  2. proportional representation voting systems (use proportional formulas) - apportionment methods such as Hare-Hamilton, D’Hondt and Sainte-Lague,

  3. mixed voting systems (combine two or more different types of electoral formulas, for example majoritarian and proportional); e.g. German mixed-member proportional system.

Types of voting systems (2)

A majoritarian electoral system is one in which the candidates or parties that receive the most number of votes win.

There are two general types of majoritarian electoral systems:

  1. plurality (or relative majority) electoral systems,

  2. absolute majority electoral systems.

Types of voting systems (3)

In proportional representation systems (PR) we use so-called divisors (denoted with d) to proportionally distribute seats.

The divisor is derived from the proportionality principle: \[\frac{s_i}{S} = \frac{v_i}{V} \forall i\]

Roughly speaking, to obtain a seat in PR, party or candidate have to gain at least as many votes as the value of the divisor. The divisor is the minimum number of votes required for a party or candidate to capture a seat.

PR methods will be discussed later in detail.

Types of voting systems (4)

The idea behind proportional representation is that a proportion of votes obtained should correspond to the proportion of seats - the number of seats won by a party or group of candidates is proportionate to the number of votes received.

Lecture 2b Majoritarian electoral (voting) systems: how to choose the winner/winners using variaties of plurality and absolute majority systems?

Majoritarian electoral (voting) systems

The table below presents the distribution of valid preferential votes (e.g.: 5 ballots: ABC, that is, A \(\succ\) B \(\succ\) C).

Voters were eligible to rank candidates so the table shows detailed preference schedule (distribution of voters’ preferences).

Ranking ABC ACB BAC BCA CAB CBA
No. of Votes 5 0 2 1 0 4

Plurality Method

With the plurality method, the winner is the candidate (or candidates) with the highest number of votes.

If there is more than one seat to obtain in electoral district, say n, the n candidates with the most votes are declared winners.

In the example, if there is only one seat available, the winner is the candidate A.

Plurality method in SMD and MMD (a few well-known variants)

FPTP

A first-past-the-post (FPTP) voting method is one in which voters indicate on a ballot the candidate of their choice, and the candidate (single-member electoral districts (SMD) are used) who receives the most votes wins. This is sometimes described as winner takes all.

Borda Count

Each voter ranks the candidates. If there are \(n\) candidates, then \(n\) points are assigned to the first choice for each voter, \(n-1\) points for the next choice, and so on (we can also assign \(n-1\) points for the first choice, \(n-2\) for the second and ... 0 for the last choice).

The points for each candidate are added and the candidate who received the largest number of points is declared the winner.

Borda Count (2)

Who is selected as the winner if we employ Borda count?

For example: the option A gets \(5*3 + 2*2 + 1*1 + 4*1 = 24\) points.

Instant Runoff Method

Instant-runoff voting (IRV), alternative vote (AV), or transferable vote is an electoral system used to elect a single winner from a field of more than two candidates.

Instant Runoff Method (2)

Employing the preference schedule:

Ranking ABC ACB BAC BCA CAB CBA
No. of Votes 5 0 2 1 0 4

No candidate captured the absolute majority (i.e. 7 first preferences), so we drop the weakest one and transfer his or her votes to the rest according to the second preferences:

Ranking AC AC AC CA CA CA
No. of Votes 5 0 2 1 0 4

Instant Runoff Method (3)

Consider another example. Now we have:

Ranking ABCD BACD BCAD DCAB CBAD
No. of Votes 4 2 1 2 5
Ranking ABC ACB BAC BCA CAB CBA
No. of Votes 4 0 2 1 2 5
Ranking AC AC AC CA CA CA
No. of Votes 4 0 2 1 2 5

The method of pairwise comparisons

In the pairwise comparison voting system, the voters rank the candidates by making a series of comparisons in which each candidate is compared to each of the other candidates.

For example, if choice A is preferred to B, then A receives 1 point. If the candidates tie, each receives 0.5 point. The candidate with the most points is declared the winner.

The method of pairwise comparisons - example

Recall the following distribution of votes:

Ranking ABC ACB BAC BCA CAB CBA
No. of Votes 5 0 2 1 0 4

Who is the winner in Pairwise Comparison Method?

Thus, B beats A, A beats C, B beats C.

Runoff Method (the two-round majority system)

With the runoff method, candidates are expected to gain a majority of votes (or absolute majority) to be declared the winner. By majority of votes, we mean receiving more than 50% of total votes. If no candidate receives the required number of votes (an absolute majority), then all but the two candidates receiving the most votes, are eliminated, and a second round of voting (runoff) occurs.

Runoff Method (2)

Ranking AC AC AC CA CA CA
No. of Votes 5 0 2 1 0 4

Approval Voting

The approval voting method allows each voter to cast one vote for each candidate who meets his or her approval.

The candidate with the most votes is declared the winner. Approval voting has also been called set voting because voters vote for whichever set of candidates they prefer versus the candidates they don’t vote for.

Some variaties of the plurality majoritarian and the absolute majority voting systems - usage

Method Usage
1 First-Past-the-Post e.g. UK, USA, Canada, Poland
2 Two-round majority system e.g. lower house elections in France
3 Instant Runoff e.g. Australia, Oscar for Best Picture
4 Borda count Nauru
5 SNTV e.g. Japan
6 Limited vote e.g. Spain
7 Block vote e.g. Poland before 2011
8 Party block vote Singapore
- - -

Voters’ preferences - voting system - election result

Assuming that a voters’ preference distribution does not change, switching between various voting methods may change the result of election - the so-called mechanical effect of a voting system.

The voting system affects the format and the mechanism of party systems.

Kenneth Arrow on voting systems and election results

Arrow shows that the result of any preference-aggregation mechanism (any voting system) depends upon the mechanism itself as well as on the preferences of the voters:

K. Arrow’s fairness criteria (1)

What would it take for a voting method to at least be a fair voting method?

Kenneth Arrow set forth a minimum set of requirements that we call Arrow’s fairness criteria:

K. Arrow’s fairness criteria (2)

Condorcet candidate

A candidate preferred by a majority of the voters over every other candidate when the candidates are compared in head-to-head comparisons is called a Condorcet candidate (named after the Marquis de Condorcet, an eighteenthcentury French mathematician and philosopher).

K. Arrow’s fairness criteria (3)

Borda count violates the majority criterion

No. of voters 6 2 3
1 A B C
2 B C D
3 C D B
4 D A A

Table shows the preference schedule for a small election.

The majority candidate in this election is A with 6 out of 11 first-place votes.

Under the Borda count method, the winner is B (32 points to A’s 29 points).

The plurality method (first-past-the-post (FPTP)) violates the Condorcet criterion

No. of voters 49 48 3
1 R H F
2 H S H
3 F O S
4 O F O
5 S R R

Plurality-with-elimination (Instant Runoff) violates the monotonicity criterion

No. of voters 7 8 10 2
1 A B C A
2 B C A C
3 C A B B

TS = 27,

Absolute majority = 14.

The winner is C.

No. of voters 7 8 10 2
1 A B C C
2 B C A A
3 C A B B

Borda count violates IIA

No. of voters 4 3 9
1 A A B
2 B C A
3 C B C

Assumption: we assign \(n-1\) points for the first choice, \(n-2\) for the second and ... 0 for the last choice.

Borda count violates IIA (2)

No. of voters 4 3 9
1 A A B
2 B B A
3 C C C

With C at the bottom, the winner is B (25 point).

We call C an irrelevant alternative in ranking A and B.

Plurality method violates the IIA

In a plurality voting system 7 voters rank 3 alternatives (A, B, C).

In an election, initially only A and B run: B wins with 4 votes to A’s 3, but the entry of C into the race makes A the new winner.

Implications of the Arrow’s impossibility theorem

The theorem implies that:

Each of the voting methods can be made to violate at least one of the fairness criteria presented above - in particular IIA.

IIA criterion is sometimes criticised for being too strong to be satisfied by any voting method.

There is no perfect voting method.

Summary of violations of the fairness criteria

Figure: Summary of violations of the fairness criteria. “Yes” indicates that the method violates the criterion (Tannenbaum 2014).

Figure: Summary of violations of the fairness criteria. “Yes” indicates that the method violates the criterion (Tannenbaum 2014).

Lecture 3: Electoral systems - methods of selection of partisan (political) and nonpartisan officials (part 2) - Proportional representation - apportionment methods

Types of apportionment methods

Remark: Proportional representation requires multi-member districts (in practice, at least 3 seats per constituency).

  1. Highest averages methods
  1. Largest remainders methods

Apportionment methods

Apportionment methods are used in order to satisfy the principle of proportional representation.

Apportionment methods (2)

In order to distribute the number of seats won by a party or group of candidates in proportion to the number of votes received, we make use of the following proportion:

\[\frac{s_i}{S} = \frac{v_i}{V} \forall i\] where:

\(v_i\) = the number of valid votes for i-th party;

\(s_i\) = the number of seats assigned to i-th party;

\(TV\) or \(V\) = the total number of valid votes;

\(TS\) or \(S\) = the total number of available seats.

Apportionment methods (3)

Transforming the equation above we obtain:

\[s_i = v_i \frac{S}{V} \text{ or equivalently } s_i = \frac{v_i}{\frac{V}{S}} = \frac{v_i}{d}\]

\(d = \frac{V}{S}\) is called a standard divisor.

Assume we have \(S = 10, V = 100, v_1 = 40\). Then, we get \[\frac{\text{?}}{10} = \frac{40}{100}\]

Of course, “?” equals 4.

Standard quota

\[q_i = \frac{v_i}{\frac{V}{S}}\]

The standard quota of a party (\(q_i\)) (sometimes called the fair quota) is the exact fractional number of seats that the party would get if fractional seats were allowed.

Apportionment methods - what does it mean that two quantities (votes and seats) are in proportion (proportional)

In general, proportion says that two ratios (or fractions) are equal. For example:

\[\frac{1}{2} = \frac{2}{4}\]

1-out-of-2 is equal to 2-out-of-4

The ratios are the same, so they are in proportion (are proportional). When things are in proportion, then their relative sizes are the same.

Apportionment methods (5)

Let us use the formula above to distribute seats from the example below.

There are 12 seats to distribute in an electoral district. 6 parties participate in elections. The table below shows the distribution of valid votes in the district.

\(i\) \(v_i\)
1 26000
2 19000
3 18500
4 16000
5 10000
6 3700
\(\sum\) 93200

Apportionment methods (6)

Let us use the formula above to distribute seats from the example below.

Then, we can write

\[q_i = s_i^{*} = \frac{v_i}{\frac{93200}{12}} = \frac{v_i}{7766.66667}\]

Apportionment methods (7)

We get:

i \(v_i\) \(q_i\) \([q_i] = s_i\)
1 26000 3.35 3
2 19000 2.45 2
3 18500 2.38 2
4 16000 2.06 2
5 10000 1.29 1
6 3700 0.48 0
\(\sum\) 93200 10 [< 12 (!)]

Hamilton (Hare) Method

In the previous example we tried to distribute seats rounding the so-called standard quota of seats to the nearest integer (whole number). Unfortunately, this approach often fails.

To resolve the problem of rounding that emerged in the previous example, we employ one of the apportionment methods, for instance Largest Remainders Methods (LRM).

Hamilton (Hare) Method (2)

Hamilton method is the most popular LRM. We employ this method to resolve the problem of rounding in proportional division of seats.

Hamilton (Hare) Method (4)

Employing Hamilton method we finally get the following distribution:

i \(v_i\) \(q_i\) \(\lfloor q_i \rfloor\) \(r_i = q_i - \lfloor q_i \rfloor\) \(s_i\)
1 26000 3.35 3 0.35 3
2 19000 2.45 2 0.45 2+1
3 18500 2.38 2 0.38 2
4 16000 2.06 2 0.06 2
5 10000 1.29 1 0.29 1
6 3700 0.48 0 0.48 0+1
\(\sum\) 93200 10 12

Jefferson-d’Hondt method

Figure: Jefferson-d’Hondt algorithm (Tannenbaum 2014).

Figure: Jefferson-d’Hondt algorithm (Tannenbaum 2014).

Webster - Sainte-Lague method

Figure: Webster - Sainte-Lague algorithm (Tannenbaum 2014).

Figure: Webster - Sainte-Lague algorithm (Tannenbaum 2014).

D’Hondt method

Remark: the result of D’Hondt apportionment \(\equiv\) the result of Jefferson apportionment

\[ quotient_{DH} = \frac{v_i}{s^*_i + 1} \]

where \(v_i\) is the total number of votes that \(i-\)th party received and \(s^*_i\) is the number of seats that a party has been allocated so far, initially 0 for all parties).

Apportionment methods - examples

Link: https://docs.google.com/spreadsheets/d/1QslIHty8AT_R7nLXiliYg4QQE2f0b7WqjWaG-eKFziw/edit?usp=sharing

A unification bonus - example

Forming an electoral alliance (a pre-election coalition), can be beneficial for the coalition and for the parties within the alliance. The alliance can get more seats than if the parties within it run for seats separately - this is because some voting methods such as D’Hondt are superadditive.

Link: https://docs.google.com/spreadsheets/d/1b3etzZhjIKbVfXKrehmjRiR-l4zIkjEyOFsH87DqfgA/edit?usp=sharing

Remark: Sainte-Lague is not superadditive.

The quota rule and paradoxes of apportionment methods

(…)

Lecture 4: Electoral systems - methods of selection of partisan (political) and nonpartisan officials (part 3)

Electoral districts - definition

Electoral district is a territorial subdivision for electing members to a legislative body.

Advantages of delimiting electoral districts (1)

  1. Geographic link between constituent and representative - electoral districts improve the accountability of representatives to their voters. Electoral districts link elected representatives to a smaller, geographically-defined, constituency. This allows voters to hold specific representatives accountable.

As multiple-member districts are made larger, this link is weaker. In party list PR systems without delineated districts, such as the Netherlands and Israel, the geographic link between representatives and their constituents is considered extremely weak.

Advantages of delimiting electoral districts (2)

  1. Electoral districts can ensure broader geographic representation in parliament. Electoral districts guarantee a geographic diversity in the legislative assembly. This generally also means that more attention is accorded to regional issues and to constituency service.

Advantages of delimiting electoral districts (3)

  1. Electoral districts would permit the use of an open party list (Open-list proportional representation systems) – difficult to manage administratively with a single national constituency, because of too many candidates (e.g. 460 in Polish lower house election)

However, the most compelling argument against delimitation is that a constituency-based system can produce substantial electoral disproportionality - in PR systems, the decrease in district magnitudes elicits the rise in electoral disproportionality.

Ballot types - a few examples

  1. FPTP
  2. Alternative vote
  3. PBV
  4. STV
  5. Closed-list PR (e.g. )
  6. Open-list PR, OLPR (e.g. Poland)

Ballot types (2)

  1. FPTP

Ballot types (3)

  1. STV

Ballot types (4)

  1. Closed-list PR

Ballot types (5)

  1. OLPR

Mechanical and psychological effects of voting systems

Voting systems affect the results of elections. Scholars distinguish mechanical and psychological effects of electoral systems.

Mechanical effect is the result of mathematical properties of a voting system; how electoral systems affect the way votes are transformed into seats in a parliament.

Mechanical and psychological effects of voting systems (2)

Endogeneity in studies on electoral systems

Mechanical and psychological effects of voting systems (3)

Plurality formulas are always associated with two-party competition except where strong local minority parties exist.

Mechanical and psychological effects of voting systems (3)

Mechanical and psychological effects of voting systems (4)

The electorate reacts to the electoral system by strategically defecting from their preferred party to a more viable party. Voter-centric psychological effects – strategic voting – have become the focal point of electoral research in recent years.

Strategic voting occurs under different electoral formulas, suggesting that voters anticipate the mechanical effects of electoral rules in various settings.

District magnitude impacts party system size - this relationship is conditioned by heterogeneity. The more seats to be filled in a constituency, the more parties are competing, the more parties receive votes and the more parties gain seats.

Mechanical effect and electoral disproportionality

Important, ‘mechanical’ predictors:

Drawing

Read more e.g.: https://www.sciencedirect.com/science/article/pii/S026137941730570X

Measuring electoral disproportionality

\[Ghi = \sqrt{\frac{1}{2}\sum(s_i/TS-v_i/TV)^2}\] where: \(s_i =\) the fraction of seats assigned to i-th party; \(v_i =\) the fraction of votes casted for i-th party.

A unification bonus (a coalition bonus)

Numerical example:

https://docs.google.com/spreadsheets/d/1b3etzZhjIKbVfXKrehmjRiR-l4zIkjEyOFsH87DqfgA/edit?usp=sharing

Mechanical effects of apportionment methods

Numerical example:

https://docs.google.com/spreadsheets/d/1QslIHty8AT_R7nLXiliYg4QQE2f0b7WqjWaG-eKFziw/edit?usp=sharing

Lecture 4: Gerrymandering and malapportionment

Gerrymandering

Figure: Gerrymandering.

Figure: Gerrymandering.

Malapportionment

Equality of voters:

\[\frac{v_1}{s_1} = \frac{v_2}{s_2} = \text{ ... } = \frac{v_i}{s_i}\]

\[\frac{s_i}{TS} = \frac{v_i}{TV} \forall i\]

where:

Ideal population

The ‘ideal’ population (\(i\)-th constituency) \(= \tilde{v_i} = \frac{TV}{TS} \times s_i\)

For SMD, the ‘ideal’ population equals the so-called standard divisor (i.e. \(\frac{TV}{TS}\)).

(…)